In a skillet over medium heat, melt the butter.
Add diced apples, brown sugar, and cinnamon.
Cook 5–7 minutes, just until softened and glossy.
Remove from heat and let cool slightly.
Grease a 9×13 baking dish.
Add half of the bread cubes to the dish.
Spoon the apple mixture evenly over the bread.
Top with remaining bread cubes.
In a bowl, whisk together eggs, milk, brown sugar, vanilla, cinnamon, nutmeg, and salt.
Pour evenly over the bread.
Gently press the bread down so everything is soaked.
Cover and refrigerate at least 4 hours or overnight.
Preheat oven to 350°F.
Remove dish from the fridge while the oven preheats.
Uncover and drizzle a little melted butter over the top (this helps create a golden, bakery-style finish).
Bake for 40–45 minutes, until puffed, lightly golden, and just set in the center.
(It should still be soft and custardy — not dry.)
Gently melt the cream cheese (microwave in short bursts or over very low heat).
Whisk until smooth.
Whisk in powdered sugar, vanilla, and 2 tablespoons milk.
Add more milk 1 tablespoon at a time until thin and drizzle-able. This is meant to be light, not thick frosting.
Spoon or slice the French toast bake onto plates and finish with a light drizzle of cream cheese glaze.
Optional: maple syrup